We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with filtering methods such as the extended and ensemble Kalman filter. We use the former to show robustness and the latter to ensure computational efficiency in the case of nonlinear models. Our method matches or outperforms other robust filtering methods (such as those based on variational Bayes) at a much lower computational cost. We show this empirically on a range of filtering problems with outlier measurements, such as object tracking, state estimation in high-dimensional chaotic systems, and online learning of neural networks.

在存在异常值和误设测量模型的状态空间模型的在线滤波中，我们导出了一种新颖、可靠证明的闭合贝叶斯更新规则。我们的方法将广义贝叶斯推理与滤波方法（如扩展和集成卡尔曼滤波器）相结合，其中前者用于展示鲁棒性，后者用于确保非线性模型的计算效率。在异常值测量的一系列滤波问题（如物体跟踪、高维混沌系统的状态估计和在线神经网络学习）中，我们在更低的计算成本下与其他鲁棒滤波方法（如基于变分贝叶斯的方法）相匹配或表现更好。

通过广义贝叶斯实现鲁棒卡尔曼滤波